For sake of the discussion, I decided to offer up the following to display that Catholics do have a justification from Scripture for the doctrine of purgatory. You may not agree with it, and most probably you won't but then again there are a few things we all disagree upon. Anyway please forgive me if I missed something or didn't answer all of your questions:
The doctrine of purgatory is relatively simple and not as complex as some here would like everyone to believe. The Catechism of the Catholic church states simply:
1030 All who die in God's grace and friendship, but still imperfectly purified, are indeed assured of their eternal salvation; but after death they undergo purification, so as to achieve the holiness necessary to enter the joy of heaven.
1031 The Church gives the name Purgatory to this final purification of the elect, which is entirely different from the punishment of the damned. The Church formulated her doctrine of faith on Purgatory especially at the Councils of Florence and Trent. The tradition of the Church, by reference to certain texts of Scripture, speaks of a cleansing fire:
As for certain lesser faults, we must believe that, before the Final Judgment, there is a purifying fire. He who is truth says that whoever utters blasphemy against the Holy Spirit will be pardoned neither in this age nor in the age to come. From this sentence we understand that certain offenses can be forgiven in this age, but certain others in the age to come.
1032 This teaching is also based on the practice of prayer for the dead, already mentioned in Sacred Scripture: "Therefore Judas Maccabeus made atonement for the dead, that they might be delivered from their sin." From the beginning the Church has honored the memory of the dead and offered prayers in suffrage for them, above all the Eucharistic sacrifice, so that, thus purified, they may attain the beatific vision of God. The Church also commends almsgiving, indulgences, and works of penance undertaken on behalf of the dead:
Let us help and commemorate them. If Job's sons were purified by their father's sacrifice, why would we doubt that our offerings for the dead bring them some consolation? Let us not hesitate to help those who have died and to offer our prayers for them.
To simplify, purgatory is a state or condition of cleansing, that occurs after the death of someone who is saved and yet is not pure enough to enter God's presence. This state of cleansing is temporal. And our prayers edify those that are in this condition.
I will try to show that we as Catholics have a basis for this belief in Scripture. But to formulate that belief it requires a little ground work. In other words a foundation needs to be laid first before one can understand the purpose of this doctrine. The foundation is the following doctrines:
1) Temporal punishment due to sin.
2) Difference between mortal and venial sin.
3) The state of purity the soul must be in to enter God's presence.
1) Temporal punishment due to sin: When Christ died upon the cross for us, He took away from us the eternal punishment due to our sin, but He did not take away the temporal punishment due to our sin. This is best illustrated in 2nd Samuel:
2 Sam 12: [13] And David said to Nathan: I have sinned against the Lord. And Nathan said to David: The Lord also hath taken away thy sin: thou shalt not die. [14] Nevertheless, because thou hast given occasion to the enemies of the Lord to blaspheme, for this thing, the child that is born to thee, shall surely die.
In this passage, God saved David from permanent death, but not from temporal punishment due to his sin. Even though God forgave David, David's son was going to die.
We also find evidence of this in Hebrews 12: [5] And you have forgotten the consolation, which speaks to you, as unto children, saying: My son, neglect not the discipline of the Lord; neither be thou wearied whilst thou art rebuked by him. [6] For whom the Lord loves, he chastises; and he scourges every son whom he receives. [7] Persevere under discipline. God deals with you as with his sons; for what son is there, whom the father doth not correct? [8] But if you be without chastisement, whereof all are made partakers, then are you bastards, and not sons. [9] Moreover we have had fathers of our flesh, for instructors, and we reverenced them: shall we not much more obey the Father of spirits, and live? [10] And they indeed for a few days, according to their own pleasure, instructed us: but he, for our profit, that we might receive his sanctification. [11] Now all chastisement for the present indeed seems not to bring with it joy, but sorrow: but afterwards it will yield, to them that are exercised by it, the most peaceable fruit of justice.
Obviously God is a just God, so He is not going to chastise or scourge those that don't deserve it. So one can safely assume that someone that is being chastised by God has done something that God doesn't like, i.e. sin.
Another passage to look at is: Mat 5: [25] Be at agreement with thy adversary betimes, whilst thou art in the way with him: lest perhaps the adversary deliver thee to the judge, and the judge deliver thee to the officer, and thou be cast into prison. [26] Amen I say to thee, thou shalt not go out from thence till thou repay the last farthing. In this passage we see that there is a requirement for sin that is not eternal.
We also see it here: Matt 18: [31] Now his fellow servants seeing what was done, were very much grieved, and they came and told their lord all that was done. [32] Then his lord called him; and said to him: Thou wicked servant, I forgave thee all the debt, because thou besoughtest me: [33] Shouldst not thou then have had compassion also on thy fellow servant, even as I had compassion on thee? [34] And his lord being angry, delivered him to the torturers until he paid all the debt. [35] So also shall my heavenly Father do to you, if you forgive not every one his brother from your hearts.
2) Difference between mortal and venial sin. This is outlined explicitly in only one place in Scripture and that is 1John 5: [16] He that knows his brother to sin a sin which is not to death (venial sin), let him ask, and life shall be given to him, who sins not to death. There is a sin unto death (mortal sin): for that I say not that any man ask. [17] All iniquity is sin. And there is a sin unto death.
This passage provides us with an understanding that there are two categories of sin: venial (sins, which is not to death) and mortal (sin unto death). It should also be pointed out here that this passage encourages us to pray for our brethren that are under the weight of venial sin and that our prayers are beneficial to those under the weight of venial sin.
3) The condition of the soul to see God. Certain passages in Scripture tell us what condition our soul needs to be in to see God.
Rev 21: [27] There shall not enter into it anything defiled, or that worketh abomination or maketh a lie, but they that are written in the book of life of the Lamb.
Heb 12: [14] Follow peace with all men, and holiness: without which no man shall see God.
Matt 5: [8] Blessed are the clean of heart: for they shall see God.
Jesus also commands us to: [48] Be you therefore perfect, as also your heavenly Father is perfect. [Matthew 5:48]
So what is this purity that is being spoken of here? Jesus isn't mincing words. He is telling us what condition we need to be in to see His Father face to face. Now here is a place where most Protestant/Evangelicals differ in our understanding of justification/sanctification and this topic is not the point of this discussion and I will not go into it here. But from the writings of Paul we know that our works shall be judged on the Day of the Lord as by fire:
1 Cor 3: [11] For other foundation no man can lay, but that which is laid; which is Christ Jesus. [12] Now if any man build upon this foundation, gold, silver, precious stones, wood, hay, stubble: [13] Every man's work shall be manifest; for the day of the Lord shall declare it, because it shall be revealed in fire; and the fire shall try every man's work, of what sort it is. [14] If any man's work abide, which he hath built thereupon, he shall receive a reward. [15] If any man's work burn, he shall suffer loss; but he himself shall be saved, yet so as by fire. [16] Know you not, that you are the temple of God, and that the Spirit of God dwelleth in you? [17] But if any man violate the temple of God, him shall God destroy. For the temple of God is holy, which you are.
Verse 13 is very explicit that Paul is talking about the day of the Lord which is our own meeting with our Judge after our deaths. In this passage the man that builds upon Christ's foundation, has to be a Christian for an atheist does not build upon an internal foundation of Christ. Those works that he has built up are revealed by fire. Verse 14 outlines those whose works remain (i.e. works of righteousness) and he gets his reward (heaven). In verse 15, some of the works of the Christian are not works of righteousness and they burn. He suffers loss, but in the end he is saved. This refers to the those enduring purgatory. Then you have those Christians in verse 17, who have violated themselves through sin and those God will destroy. So here we see the rewards/punishments of heaven (14), purgatory (15), and hell (17).
Another passage that I believe support purgatory is:
Mat 12: [31] Therefore I say to you: Every sin and blasphemy shall be forgiven men, but the blasphemy of the Spirit shall not be forgiven. [32] And whosoever shall speak a word against the Son of man, it shall be forgiven him: but he that shall speak against the Holy Ghost, it shall not be forgiven him, neither in this world, nor in the world to come.
Purgatory and praying for the dead are tied to the hip and as such both support each other. So is praying for the dead Biblical? I say the answer is yes. The first passage comes from 2nd Maccabees, which I know is no longer in Protestant Bibles. But for the sake of the argument is important to point out that the Catholic church retained this book within its canon and views it as Canonical.
2 Mac: [39] And the day following Judas came with his company, to take away the bodies of them that were slain, and to bury them with their kinsmen, in the sepulchres of their fathers. [40] And they found under the coats of the slain some of the donaries of the idols of Jamnia, which the law forbiddeth to the Jews: so that all plainly saw, that for this cause they were slain. [41] Then they all blessed the just judgment of the Lord, who had discovered the things that were hidden. [42] And so betaking themselves to prayers, they besought him, that the sin which had been committed might be forgotten. But the most valiant Judas exhorted the people to keep themselves from sin, forasmuch as they saw before their eyes what had happened, because of the sins of those that were slain. [43] And making a gathering, he sent twelve thousand drachms of silver to Jerusalem for sacrifice to be offered for the sins of the dead, thinking well and religiously concerning the resurrection, [44] (For if he had not hoped that they that were slain should rise again, it would have seemed superfluous and vain to pray for the dead,) [45] And because he considered that they who had fallen asleep with godliness, had great grace laid up for them.
This passage outlines the ancient doctrine of praying for those that have passed on in hope of their resurrection, which it should be noted that not only do Apostolic Christians pray for the dead; but THE JEWS STILL FOLLOW THIS ANCIENT PRACTICE.
We also find in the writings of Paul a few interesting passages:
1 Cor 15: [29] Otherwise what shall they do that are baptized for the dead, if the dead rise not again at all? why are they then baptized for them? [30] Why also are we in danger every hour? [31] I die daily, I protest by your glory, brethren, which I have in Christ Jesus our Lord.
1 Tim 1: [16] The Lord give mercy to the house of Onesiphorus: because he hath often refreshed me, and hath not been ashamed of my chain: [17] But when he was come to Rome, he carefully sought me, and found me. [18] The Lord grant unto him to find mercy of the Lord in that day: and in how many things he ministered unto me at Ephesus, thou very well knowest.
In the first passage quoted Paul is speaking of some form of practice that we have no information concerning, which refers to the ability of the living to do something that benefits those that have passed on. He also is using the doctrine of the resurrection of the dead to provide justification for this practice.
In the 2nd passage, Paul is referring to Onesiphorus in the past tense and not present as he does with others that he names. From the usage of past tense one could assume that Onesiphorus has already fallen asleep at the writing of this letter. Notice verse 18. Paul is praying that Onesiphorus finds the mercy of the Lord in that day. What day?
The point I am trying to make here is that we do have a justification of our belief from Scripture. You may not agree with my interpretation of these passages, but then again that is expected and I respect that.